University crashes

The optimal size of a university is always a little bit bigger than its actual size. More precisely, the size of a university doesn't really matter. What does matter is whether it's growing or shrinking. A growing university is easy to manage. If you need to grow one department relative to another, you hire people in one department and don't hire them in another. A constant sized university is harder to manage. If you need to grow one department relative to another, you hire people in one department and fire them in another. It's easier to not hire than to fire. And a shrinking university is very hard to manage.

Suppose the overall market is growing at 2%, and the number of universities is fixed. Each university can grow at the same 2%, and every university is easy to manage. Something like 2% growth, plus normal attrition through retirements, is normally enough to handle fluctuations of relative demand between departments without actually firing anybody. So we can have an equilibrium where each university is growing at 2%, and no university wants to grow faster or slower than 2%. Assume we are in that equilibrium.

What happens if the overall market stops growing?

Then it gets nasty. Just because the overall market stops growing doesn't mean each individual university will stop growing. Each individual university can cut its admissions standards slightly, relative to other universities, and grow while the other universities contract. But what happens in the Nash equilibrium, when all universities do the same?

1. The elasticity of student demand for an individual university, with respect to admissions standards, is quite high. By cutting admissions standards it can get students who would have gone to other universities, as well as students who would not have gone to university at all. But the elasticity of student demand for all universities together is much lower. They can only attract additional students who would not have gone to any university.

2. Plus, even though each university cares a bit about the absolute level of its admissions standards, it cares much more about its own admissions standards relative to other universities' admissions standards.

Adding 1 and 2 together we get a strong multiplier effect. Each university faces a trade-off between size and admissions standards. Other things equal, the higher its admissions standards the smaller the number of students admitted. But its own chosen point on that trade-off -- what admissions standards to set -- depends on what other universities choose. An exogenous 1% drop in admissions standards by other universities will lead each university to want to cut it's own admissions standards by (say) 0.9%. There's positive feedback. Positive feedback creates a multiplier. The multiplier in this case will be [1/(1-0.9)] = 10.

What does a multiplier of 10 mean? It means that the effect of a drop in demand at an individual university on its admissions standards will be multiplied by 10 if the same drop in demand hits all universities. The drop in admission standards will be 10 times bigger at the aggregate level.

Now, we are not talking about a drop in demand. But we are talking about a drop in the growth rate of demand. And since each individual university doesn't want to stop growing, it will cut admissions standards in response, hoping to grow while others shrink. But all universities will do the same. But then each university will want to drop its admissions standards even further. Both because admissions won't increase very much if all universities cut admissions standards; and because it's OK to cut standards if every other university is cutting its standards too, because your relative standards are still OK. And then there's a second round of the multiplier process. And so on.

So, if demand stops growing, there will be a desperate scramble for students. The sort of actions that one university would take if its own demand stopped growing will be multiplied by 10 if demand for all universities stops growing.

Don't take that number 10 too seriously. I just made it up. I don't know what the real number will be. It might be bigger or smaller than 10. But it will be bigger than 1.

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I think this is true. Trent University is a prime example of this, they have been in deficit for years. They can never seem to attract enough students to pay their bills or cut enough to get their budget under control.

What happens to any business whose inputs are
fixed
non-fungible
time-intensive in their production
depreciating at a slow rate ( long-lived)?

Once you leave the universe of fast dying peasants cultivating land with almost no equipment and enter a world of costly machinery and a workforce that needs years of training and cannot be turned into something else ( pace Ricardo, it's been a long time since a vintner could turn to cloth manufacturing or a quantum physicist into a neurosurgeon, could have been but wrong career choice), it's grow or grow for everybody save the corner store.

This week take-home for 10 points:
Compare the economics of universities and airlines. ( Use the word "crash" with extreme care.)

Interesting. Mind you, in much of the country, the decline in local university populations has been procedding for for four or five years now with no signs of the outcomes you mention here. So long as shortfalls in the local supply of students can be offset by recruitment of international students, there's no fall in the overall market.

Actually, this reminds me of another phenomenon, and I wonder if people have looked into it. In Germany, where the number of young people entering the labour market is falling, there are coming crises, in branches that were static for years (teachers and skilled tradesmen) because the static demand meant relative low rates of recruitment. Now the average age of teachers and skilled tradesmen is over 50. So now lots of kids will be trained in these skills and join the "booming" profession - until the next statis comes. Has anybody studies these waves of generational employment?

One way to solve this problem is incenting professors who choose to "retire" or transfer to universities with different hiring patterns. On the student side, one could tinker with tuitions or admission standards on a department basis on order to counter relative changes. But ultimately, given the overall structure, the long-run outcome may be for some departments to shut down. The economics literature on two-sided markets may be useful here.

Of course, one way to compete without dropping admission standards -- and so improve your standing relative to universities that do drop their standards -- is to build out more student facilities. Fancier dorms, more gym space, more special programs, etc. Just like lowering admission standards, that's an arms race as well with the advantage going not to those who spend, but to those who spend more than their (otherwise) peers.

It seems like we've been seeing that type of feedback roughly since the baby boomers past college age.

I don't understand the context. Undergraduate applications and enrollement in Ontario Universities has been going steadily upward (with a blip in 2003). Is there a decline in applications on the horizon in Ontario?

Alex makes a good point. Here in PEI I don't think we've met the point yet where local students are in decline, but its clear that international students can probably make up a good bit of the difference when they do. Given continued shortfalls in capacity in some Canadian regions we can tap into that market as well.

But on the broader issue, I don't think we need to lower our standards to get more of the local population, the High Schools are doing it for us. That and the expectations of the labour market, which convince more and more students that they need a credential to get in. If anything, we'd need to continually raise our admission standards to keep the quality of students constant.

Given that, I think the other standards issue is our marking and program standards. We're getting more and more students who don't measure up to our older expectations, or who aren't as suited to our existing programs - what do we do with them? Fail them out and bring admin down on our heads? water down our marking and program standards so most get through? Or find a way to stream or divert them as appropriate to versions of programs or different programs that suit them better.

Jim, on the "everything is going to hell in a handbasket front" my son pointed out this example to me. This is from a grade 12 data management course intended for students on a university stream:

1. The variables student height and grade in mathematics have
a. a positive correlation c. an inverse correlation
b. a negative correlation d. no correlation

The teacher told the students that the correct answer was (d). Of course, given a real world data set, the correlation between two variables will never be precisely and exactly zero. Even if there is no relationship for the population as a whole, in a sample of 30 students, one might have 3 exceptionally tall/short and high achieving/low achieving students who create a positive/negative relationship for a particular class.

Moreover, if math grade and height are both correlated with a third variable, e.g. gender, ethnicity, socio-economic status, childhood nutrition, a correlation will be observed in the data.

I thought of writing a post on that question but it would be like, what's the expression, shooting fish in a barrel?

The context is my fear that enrolment cannot keep growing forever. Canadian demographics (except in Toronto and Vancouver, IIRC) are not favourable. Much of the enrolment growth over the decades has come from increasing participation rates, rather than growth in the typical university-age population. Participation rates cannot keep growing forever. Sometime they will stop. I am worried about what will happen when they do stop. I do not know when they will stop, and if it will be a sudden stop. My hunch is that it might be soon, and it might be sudden. My hunch is that gender will play a role in this stop too. Girls' participation rates (which have accounted for a lot of the increase in past decades) will eventually stop increasing, and boys' might decline. (Frances may be posting on this soon?) I have nothing solid to back these hunches (except of course, the mathematical fact that participation rates cannot exceed 100%). But universities need to be ready for it. We cannot invest the way we would if we were sure that growth would continue forever.

Alex Usher (commenting above) keeps track of these things better than I do. I confess I had forgotten foreign students as a possible source of growth.

Having looked at reports on this over the decades, I think I can safely say that people have been saying that participation rates can't go much higher for decades now. And they keep going higher. One element, though it brings other problems with it, is the expansion of graduate programs. Everyone already has a degree? Get them to do two! or three! The other thrust I see coming is the turning of all kinds of training in things we never would have considered our territory into "degree programs', backed up by hiring practices that emphasize credentials and everyone's fear of not having that all important post secondary piece of paper.

In combination with international, I think the issue Universities will really be dealing with over the next decade or so is not declining enrollment, but declining numbers of those with the interest and aptitude to do our traditional programming, and a growing horde without, but who we're expected to deliver something to.

On my long journey back from Denver, I had some interesting conversations with fellow sufferer Loretta Fung. She teaches at an English-speaking university in Taiwan. What's fascinating to me is that they're now attracting foreign students from India, Africa, etc., etc., so this lock that N. American/European/Australian universities have on the foreign student market is looking fragile... Then again, China has its own demographic issues.

Jim -- What evidence is there that Ontario high schools are lowering their standards? Or, in your case, PEI?

In Ontario, using EQAO data, outcomes are improved since 2000 and steady since 2005. Using PISA data, Ontario is steady or improved since 2000, and only Alberta shows a decline. I donT' see evidence of high schools lowering standards.

This is just from googling. You (and especially Alex Usher) may have acccess to more data sources.

What about price? Currently (2005-2009, I am unaware of the current framework since I finished a stint on the board of governors) most universities in Ontario increase price (tuition fees) to the maximum allowable increase for incoming students. If we really start to see falling enrollments, we may also see falling tuition fees in real terms.

Alex: International students are not a endless supply for all Canadian Universities. The mid-sized Ontario University I was at had an easy time attracting international graduate students, but not international undergraduates. They had relatively low international tuition fees and domestic undergraduates were much more profitable if tuition fees and prov funding were taken into account.

@Determinant: I have no specific knowledge about Trent's situation, but its been my experience at another Ontario university that the structural deficit had more to do with flat-lined provincial funding (not indexed to inflation), crazy pension obligations, and interest payments (loans taken to build capital to service the double cohort).

If Ontario universities want to reduce price, they increase scholarships instead. A scholarship increase is like a price cut, but can be targeted at those students the university most wants to attract.

Young man - I'd have to go looking if you want hard evidence. I'm going by personal observation, and I'm looking at a much longer time span - like thirty years. Alex or someone like Torben Drewes might have a better idea of documented numbers.

Interesting ideas and exchange. Of course, as some posters will recall, we had some experience with this at Carleton in the 90's. That experience doesn't quite back all of Nick's contentions; of course it doesn't refute them either. One which can definetly be proclaimed true is that it is easier to manage a growing university than a shrinking one. But how to get a growing university?

Recall the scene at Carleton in the early 90's: lousy entry averages, huge first year classes, in 1992, second in size only to U of T in all of Ontario. So far, so good for the hypothesis. But then: huge drop out (=flunk out) rates- like 35-40% - lousy teaching conditions due to poor students, overcrowded classes, hundreds, nay thousands, of massively unhappy ex-students bad mouthing Carleton far and wide, demoralized faculty, etc etc. Net result by 1994: catastrophically falling application and enrolment rates. Indeed Carleton almost made it through the funding corridor floor which would have been a first for an Ontario university. So Senate gambled that raising the entry average would actually increase the pool of applicants, not to mention improving the classroom environment. After all, things couldn't get much worse. With a lag of only two years at most, the relative-to-the-system number of Carleton applications turned around and, gratifyingly the new applicants had better averages. Enrolment increased nicely, classroom environment improved and crisis was over,well,to the extent university crises are ever over.

Of course the overall pool was increasing at that time so I can't claim to have refuted the hypothesis, but I would suggest that in a static or slightly expanding pool, making the "goods" more desirable can overcome the elasticity of applications with grades and that it isn't necessarily true that the best strategy for all is to follow the crowd. It almost never is.

Thanks Rick. Yes, the Carleton experience in the 90's was interesting. I was actually starting to write about that "Groucho Marx effect" in the blog post, then changed my mind. Maybe I should have kept it in.

When an individual university lowers it's admissions cutoff, relative to other universities, there are two effects: 1. some students who wanted to come but were below the cutoff now come; 2. other students who were above the cutoff decide not to come because they believe, correctly, that the average quality of students will fall. The net effect can go either way. The "demand curve" (if we think of the admissions cutoff as analogous to price, which it is only up to a point) can be backward bending.

And what's doubly interesting to me is that that second effect has it's own internal multiplier. If some high quality students go elsewhere, that reduces the average quality of the remainder, and induces more high quality students to go elsewhere. We saw that feedback loop operating in reverse, with a short lag, at Carleton. And you can even end up with multiple equilibria.

But if there's a drop in demand (or a drop in the growth rate of demand) for *all* universities, the effects will be different. My guess is that the very top ones will cut admissions standards first (because Groucho Marx can't go anywhere better), and that allows the second best to cut, and the cuts will sort of trickle down the chain.

Universities can increase demand by cutting the price. A combination of lower price and higher admissions standards would have a lot of appeal. But they will probably just screw around until a new competitor arrives to eat their lunch. People are already suspicious of the cost of education. Rightfully so I think, given the enormous increase we have seen over the last 10-15 years.